I like to prechop my broccoli, cauliflower, etc, but I leave them dry and unrinsed until just before use in a tupperware or ziploc. I've heard that washing speeds rot, and I've had good luck with my dry method - though I wouldn't recommend it for all veggies.
Other veggies (like bell pepper), I have chopped and frozen. I just usually toss it in cold to whatever recipe.
I have seem some microwave steamers that have a smaller strainer insert inside of a larger tupperware that may work for you.